Kriging: a method of estimation for environmental and rare disease data

Abstract

Abstract Most properties that are distributed in geographical space vary, and often in a complex way. The information available is usually fragmentary, but we often want to know the values at intermediate locations. This is the case for both environmental and disease data. However, the nature of the data and the information that we require from them ultimately can be quite different. For rare disease knowing its spatial distribution is often not enough, we also want to know the variation in the underlying risk. At present direct links between disease and factors in the environment are tenuous; however, there is increasing interest in obtaining more precise evidence. Geostatistics provides us with a means of analysing both kinds of data underpinned by the same body of theory, the Theory of Regionalized Variables. Two types of geostatistical estimation are described here. Disjunctive kriging for estimating the probabilities of exceeding particular threshold values in the environment: it is illustrated with an example of soil salinity in Israel. Standard geostatistical technique has been adapted to analyse the spatial distribution of a rare disease, and to estimate the risk of developing it: this is illustrated with an analysis of childhood cancer in the West Midlands Health Authority Region where the risk appears largest in rural areas. The aim in the future is to use the information from both approaches to identify areas for further investigation concerning the aetiology of certain diseases.